Goal seeking using Prophet

I'm using Prophet to generate counterfactual forecasts based on varying inputs (exogenous variables). Eventually, I'd like to set a target forecast (say 10% growth of sales +/- 2% over a month period) and some constraints on the input ranges, and have some notion of _best_ combination of inputs to achieve said goal, ideally with distributions as well.

I could of-course sample uniformly over the input space and guess and check, alternatively I could run some optimizer. I feel that MCMC should give me a more principled approach to goal seeking but I'm not sure what to even look for. I'm not opposed to getting into the plumbing or tweaking the library to get this functionality but would like some help to get started.